1) Can the phrases "on one's stomach" and "on one's face" be deemed as interchangeable? They seem semantically same (being on the same side of the body) but I still feel they must be different somehow.

2) How would we translate these phrases in German? I found "bäuchlings" for the stomach part, but there doesn't seem to be a translation for the former. Is the literal translation of "auf dem Gesicht" appropriate? Physically, my face is below me, so a literal approach seems shady to me.